First off, you should watch the movie. It's also on Netflix (or at least recently was—I haven't checked in a little while) but it's listed separately. This is kind of a shame; in format, I think that it was originally a three-episode arc that was put together as a "fix-up" as a single thing.
So start there.
Let's see... Season 1 episodes. I've combined multi-episode arcs as a single bullet point. The ones I recommend have comments following and are bolded.
- "Rising Malevolence", "Shadow of Malevolence" "Destroy Malevolence"—absolutely watch this three-episode arc. Great visuals, and a wonderful concept.
- "Downfall of a Droid", "Duel of the Droids"
- "Bombad Jedi"
- "Cloak of Darkness"—I recommend this one. A prison break by the villains that goes right. Pretty fun.
- "Lair of Grevious"—I'm not normally a fan of "space dungeoncrawls" but this one is pretty cool. It follows immediately on the heels of the last episode.
- "Dooku Captured", "The Gungan General"
- "Jedi Crash", "Defenders of the Peace"
- "The Hidden Enemy"
- "Blue Shadow Virus", "Mystery of a Thousand Worlds"—an interesting germ warfare concept, with a quest for a McGuffin. Worth a watch, if nothing else for hearing Michael York's crazy alien Dr. Mengele voice.
- "Storm over Ryloth", "Innocents of Ryloth", "Liberty on Ryloth"
- "Hostage Crisis"—the introduction of the bounty hunters (which was the subtitle for the second season) and showcases how competent they can be.
- "Holocron Heist", "Cargo of Doom", "Children of the Force"—this arc actually starts off strong, but kind of peters out before it's done. I still recommend it, though.
- "Senate Spy"
- "Landing at Point Rain", "Weapons Factory", "Legacy of Terror", "Brain Invaders"—following "Senate Spy" and building off of information, this long arc is quite military in nature, for the most part, but showcases how a wide variety of stories can be told in the genre. The first one is a "space Normandy invasion", followed by a fortress infiltration, followed by an alien zombie outbreak, followed by an Attack of the Body Snatchers type story.
- "Grievous Intrigue"—a rescue mission is anticipated and turned into a trap. Not quite sure exactly how they relatively easily sprung the trap, but it's still an interesting story. Almost any story that features Grievous as the main villain are worth watching. The next episode follows it, but is not integral to the same story arc.
- "The Deserter"
- "Lightsaber Lost"
- "The Mandalore Plot", "Voyage of Temptation", "Duchess of Mandalore"—the "peaceful" Mandaloreans are both hoaky and irritating, but the villains here are, of course, the traditional Mandaloreans. Anything with them is also a must-watch.
- "Senate Murders"
- "Cat and Mouse"
- "Bounty Hunters"—a retelling of The Seven Samurai. You already know the story, but seeing the bounty hunters that they used to replace the samurai is good for a laugh.
- "The Zillo Beast", "The Zillo Beast Strikes Back"—this time, they make a space Godzilla.
- "Death Trap", "R2 Come Home", "Lethal Trackdown"
- "Clone Cadets"
- "ARC Troopers"—invasion of Kamino. Highly recommended.
- "Supply Lines"
- "Sphere of Influence"
- "The Academy"
- "Evil Plans"
- "Hunt for Ziro"—notable for the presence of Quinlan Vos, a kind of fan favorite throwaway character. But it's also a great crime story.
- "Heroes on Both Sides"
- "Pursuit of Peace"
- "Nightsisters", "Monster", "Witches of the Mist"—I'm not sure if this is an arc, or just linked stand-alone episodes, but they're all great. Plus, they set the stage for Darth Maul to eventually return.
- "Overlords", "Altar of Mortis", "Ghosts of Mortis"
- "The Citadel", "Counter Attack", "Citadel Rescue"—military strike force and spy action. Fun stuff.
- "Padawn Lost", "Wookie Hunt"—the best season finale arc so far. Highly recommended.
- "Water War", "Gungan Attack", "Prisoners"—an interesting story arc, mostly because it manages to take place almost entirely underwater.
- "Shadow Warrior"
- "Mercy Mission"
- "Nomad Droids"
- "Darkness on Umbara", "The General", "Plan of Dissent", "Carnage of Krell"—this lengthy 4-part story arc is pretty cool because it introduces a very different environment, and the Umbarans are a nifty new edition with nifty new technology. A great example of how individualized various worlds can be; this is even more true in AD ASTRA than in Star Wars, where bulk drives are not nearly as convenient and easy as Star Wars hyperspace travel. Otherwise, however, the story is probably too military to be of much use as inspiration for anything else not overtly military.
- "Kidnapped", ""Slaves of the Republic", "Escape from Kadovo"
- "A Friend in Need"
- "Deception", "Friends and Enemies", "The Box", "Crisis on Naboo"—another lengthy arc, with Obiwan going undercover with a group of bounty hunters. I'm not sold on the "space Tomb of Horrors" episode in particular, but otherwise, I quite like this particular story.
- "Massacre"—the Sith decide to eliminate the Nightsisters. Brilliant episode. One of the better ones. Really showcases the overt magico-fantasy aspect of the Star Wars setting too.
- "Bounty"—a train heist/kidnapping. A classic tale recast in the Star Wars milieu, which is really a big part of what Star Wars was always all about.
- "Brothers", "Revenge"—the return of Darth Maul! As if that wasn't a good enough reason to watch these two, it's also just a great story. An even better season finale than season 3's.
Season 5 (Note that original broadcast order is different than DVD and Netflix order)
- "A War on Two Fronts", "Front Runners", "The Soft War", "Tipping Points"
- "The Gathering", "A Test of Strength", "Bound for Rescue", "A Necessary Bond"
- "Secret Weapons", "A Sunny Day in the Void", "Missing in Action", "Point of No Return"
- "Revival", "Eminence", "Shades of Reason", "The Lawless"—I'm just going to come right out and say it; this story arc of four episodes is the PEAK of this show. They were the best. This is the best Star Wars we've seen since The Empire Strikes Back and the only thing as good (maybe) that we've seen since is Rogue One. Watch these episodes. Absolutely.
- "Sabotage", "The Jedi Who Knew Too Much", "To Catch a Jedi", "The Wrong Jedi"—Dave Filoni, at least, if not necessarily anyone else, could see through the weaknesses in Star Wars. He even realizes that the Jedi have lost their way and are not the paragons of virtue that Lucas held them out to be. In at least some small measure, this story arc redeems much of what went wrong with Star Wars over the years.
The Lost Missions (Season 6)
- "The Unknown", "Conspiracy", "Fugitive", "Orders"—an interesting spy/intrigue arc in which trooper Fives (known from many episodes throughout the show so far) discovers the trip switch for Order 66.
- "An Old Friend", "The Rise of Clovis", "Crisis at the Heart"
- "The Disappeared, Part I", "The Disappeared, Part II"
- "The Lost One", "Voices", "Destiny", "Sacrifice"—an interesting tale that starts out with a thriller/mystery as Anakin and Obiwan find clues that would expose the Sith plot (which of course have to be suppressed so that Revenge of the Sith can take place as normal) and morphs into Yoda discovering more of the history and nature of the Force.
There are a number of story arcs that never made it into becoming episodes exactly, but they were presented to fans in another format so at least we can see what the episodes might have looked like had they been made.
- Darth Maul: Son of Dathomir—on the final fate of Darth Maul's Mandalorean army, and its removal as a force by General Grievous under the direction of Darth Sidious. Terribly unfortunate that these four episodes were never made.
- "A Death on Utapau", "In Search of the Crystal", "The Big Bang"
- "The Bad Batch", "A Distant Echo", "On the Wings of Keeradaks", "Unfinished Business"—sadly, you can only watch these are youtube "roughs", but this is a great set of episodes, with a kind of Star Wars version of the Dirty Dozen sneaking around and doing military spy/sabotage and rescue missions. Highly recommended.
- Dark Disciple
That last is a novel. Avoid at all costs. It turns out that it's a Romance novel. Absolutely horrible.